: This project proposes a new paradigm for the study of how the dynamics of brain activity are related to behavior. An interdisciplinary bioengineering approach will be used to integrate the theory of nonlinear dynamics with both the analysis and design of functional magnetic resonance imaging (fMRI) experiments. This will lead to the development of new algorithms specifically targeted to the analysis of dynamic fMRI studies. The algorithm development will allow the implementation of novel fMRI experiments that are no longer limited to subtractive designs. In the past, the predominate approach to studying human cognition has been the subtractive experimental design. This method relies upon the establishment of discrete cognitive states, with the data analysis aimed at identifying brain regions that show significant changes in activity between the states. While successful in identifying brain regions that are differentially activated, the subtractive approach does not reveal the more complex temporal choreography that must occur to produce a specific behavior. To go beyond spatial mapping, one would like to know not only which brain regions are activated in a specific cognitive state, but how the pattern of brain activity makes the transition from one state to another. To do this, a new technique, called continuous fMRI is proposed. In contrast to the approach of designing experiments in which discrete behavioral states are maintained for blocks of time, this method maintains a single cognitive "state," but continuously varies a single parameter of the task. Pilot data from a continuously varying finger tapping task will be presented that demonstrate the feasibility of this approach. Continuous fMRI experiments generate dynamic data sets. New methods of analysis will be developed to characterize the types of dynamic behavior that occur. 1) Coupled with continuous fMRI, bifurcation analysis will identify state transitions in the brain as a single experimental parameter is continuously varied. Bifurcation theory will allow the classification of these transitions into one of four well-described forms. 2) Using finger tapping as a prototype task, bifurcation theory will be used to analyze the transition from low tapping rate to high tapping rate. 3) The technique will be extended to include the cognitive process of uncertainty detection. Using measures of information transmission, the amount of stimulus uncertainty will be varied in a reaction-time task, and bifurcation analysis will identify the types of state transitions that occur between low and high uncertainty. The integration of bifurcation theory with continuous fMRI is anticipated to have a significant impact on the way in which fMRI experiments are conducted and will yield new techniques for the study of neuropsychiatric illness.